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TOKYO, Feb 25 (Reuters) - The Nikkei average advanced to a four-week closing high on Tuesday after a rally in Wall Street shares to historic highs triggered short-covering in battered Japanese stocks. The Nikkei rose 1.4 percent to 15,051.60, its highest close since Jan. 29. It has recovered more than 40 percent of its losses since it fell from a six-year peak hit in late December. Shares of Softbank Corp climbed to their highest in a month on a report that the company is seeking to buy a stake in Line Corp, a mobile-messaging service controlled by South Korea's Naver Corp. The broader Topix index rose 1.2 percent to 1,233.66. The JPX-Nikkei Index 400, an index launched this year comprising firms with high return on equity and strong corporate governance, rose 1.2 percent to 11,159.39.